Hi
Thanks, Markiyan, for posting the info regarding the previous comparison 2 years ago, between Mathematica 8 and Maple 15. The way I see this comparison, two things step forward:

• Mathematica: has weaknesses with nonlinear equations and with linear equations that have nonrational coefficients. The slowness of their solver is prominent. They have known about all this for more than 10 years but the status of things doesn't seem to improve.
  
  
• Maple: is strong in solving linear and nonlinear ODEs for more than 10 years and is getting stronger at every release by developing original algorithms beyond Kamke's book. This is not a minor thing. Give a look at the pages ?updates,Maplexx,DE for xx from 8 to 16 and also to ?updates,Maple7,symbolic. 

One could argue that these observations are not really "news", that one could infer the same from the previous comparison two years ago. It is true. Still I think it is a relevant piece of information to confirm that this continues to be the case today (2013), that Maple is far ahead of Mathematica in solving differential equations also using the latest Maple and Mathematica releases.

Edgardo S. Cheb-Terrab
Physics, Maplesoft

This tweak in the new (rewritten) simplify/conjugate resulted easier than expected. The change is in place and available for download in the usual  the "Maple Physics: Research & Development" webpage.

Edgardo S. Cheb-Terrab
Physics, Maplesoft

This tweak in the new (rewritten) simplify/conjugate resulted easier than expected. The change is in place and available for download in the usual  the "Maple Physics: Research & Development" webpage.

Edgardo S. Cheb-Terrab
Physics, Maplesoft

@Andriy 

I'm glad to see that, both, you got this working the way you need and we got these commands enhanced in different ways. Looking at your coefficients.mw it also springs to my mind that some of your requirements could be options to Coefficients, as in Coefficients(expression, PhysicsType:-xxx) to select all the coefficients of objects of type PhysicsType:-xxx, further allowing to indicate the degree(s), as in Coefficients(expression, PhysicsType:-xxx, N), where N is explained in the Calling Sequence in ?Physics[Coefficients]. That would have saved the need for coding the coeffxxx functions you show in the mw. I will implement this as soon as I find some free time.

Edgardo S. Cheb-Terrab
Physics, Maplesoft

@Andriy 

I'm glad to see that, both, you got this working the way you need and we got these commands enhanced in different ways. Looking at your coefficients.mw it also springs to my mind that some of your requirements could be options to Coefficients, as in Coefficients(expression, PhysicsType:-xxx) to select all the coefficients of objects of type PhysicsType:-xxx, further allowing to indicate the degree(s), as in Coefficients(expression, PhysicsType:-xxx, N), where N is explained in the Calling Sequence in ?Physics[Coefficients]. That would have saved the need for coding the coeffxxx functions you show in the mw. I will implement this as soon as I find some free time.

Edgardo S. Cheb-Terrab
Physics, Maplesoft

@Carl Love and Alejandro

Thanks for the info, so this macro suggested fixed the problem - I think I then know what is causing it. I'll fix it at its root in the first Physics update this week.

Edgardo S. Cheb-Terrab
Physics, Maplesoft

Hi

I use a macintosh, perhaps you do not and this is why I am unable to reproduce it. Could you please enter, at the maple prompt, the following: macro(``=``, ` ` = ` `) and let me know whether it fixes the problem. 

Edgardo S. Cheb-Terrab
Physics, Maplesoft

Hi

Maple 17.02 is available for download.  Just to note that 17.02 includes various improvements in 'Physics', basically all the work done in the package till August 20, though none of the posterior improvements mentioned here in Mapleprimes, available for download at the Maple Physics: Research & Development updates page (latest update: today). These posterior improvements are described in the PhysicsUpdates.mw distributed within the zip file together with the update.

Edgardo S. Cheb-Terrab
Physics, Maplesoft

@Andriy 

In the help page you read "The select(e, f) selects the operands of the expression e which satisfy the Boolean-valued procedure f". The key observations are that you select "the operands" and you do not change the container - ie the type of the e containing the operands (but for some special cases of automatic simplification: e.g. the product of a single operand `*`(a)  becomes the operand itself and so it is not a product anymore).

Now in your last reply, phi = Ket(psi, 1, 1, 0). So select(phi, commutative) will return Ket(1, 1, 0) (because only psi is not commutative), then select(type, phi, PhysicsType:-Ket) will return Ket() because none of psi, 1, or 0 are of type PhysicsType:-Ket. Understanding those you also understand how the other results you show are formed.

In brief, that is how select works, give a look please at the help page ?select and its examples.

Edgardo S. Cheb-Terrab
Physics, Maplesoft

@Andriy 

In the help page you read "The select(e, f) selects the operands of the expression e which satisfy the Boolean-valued procedure f". The key observations are that you select "the operands" and you do not change the container - ie the type of the e containing the operands (but for some special cases of automatic simplification: e.g. the product of a single operand `*`(a)  becomes the operand itself and so it is not a product anymore).

Now in your last reply, phi = Ket(psi, 1, 1, 0). So select(phi, commutative) will return Ket(1, 1, 0) (because only psi is not commutative), then select(type, phi, PhysicsType:-Ket) will return Ket() because none of psi, 1, or 0 are of type PhysicsType:-Ket. Understanding those you also understand how the other results you show are formed.

In brief, that is how select works, give a look please at the help page ?select and its examples.

Edgardo S. Cheb-Terrab
Physics, Maplesoft

@Andriy 

Just to point out that a new Physics:-Library:-Add command, free of these subtleties regarding the evaluation of arguments of sum or the use of local variables inside procedures related to add, is ready and included in today's Physics update.

Edgardo S. Cheb-Terrab
Physics, Maplesoft

@Andriy 

Just to point out that a new Physics:-Library:-Add command, free of these subtleties regarding the evaluation of arguments of sum or the use of local variables inside procedures related to add, is ready and included in today's Physics update.

Edgardo S. Cheb-Terrab
Physics, Maplesoft

The typesetting of Physics:-Library:-Add as a sum is finished and included in today's update of Physics.

Edgardo S. Cheb-Terrab
Physics, Maplesoft

The typesetting of Physics:-Library:-Add as a sum is finished and included in today's update of Physics.

Edgardo S. Cheb-Terrab
Physics, Maplesoft

@Andriy 

Regarding these other two questions you do in "Key issue": SortProducts has an option, evaluateexpression, so that after sorting the expression is evaluated. The difference when you use this option is that, when you evaluateexpression, a product `.`(A, B, C, D) becomes `.`(A, `.`(B, `.`(C, D))). At some point (years ago) it was relevant to keep `.` as a function of two arguments. I'd need to revise this to tell you exactly why was that ... or even if it is necessary today. Actually, if it is not necessary anymore, just remove it and keep the syntax as in `.`(A, B, C, D), the same way we do with Physics:-`*`.

Regarding your other question, given an expression that involves N products, say P[j] with j from 1 to N, and where each of these P[j] has a commutative factor that you called A[j], mutliplicating a noncommutative factor - say NC[j]. So say your expression is of the form ee := Sum(A[j] * NC[j], j=1..N), and let's suppose that the NC[j] involve both Physics:-`*` and Physics:-`.`. You want to get all the A[j]. There are simple ways of doing this systematically, but we would need another Library routine to unnest products in expressions - I will prepare it, include it in the next update of Physics this week and reply here again showing you how to do this.

Edgardo S. Cheb-Terrab
Physics, Maplesoft